Generally, rare-earth magnets are commonly used in motors and generators because they allow the motors and generators to be more compact in size. However, the supply of rare-earth magnets is not sustainable due to limited availability and skewed supply locations. Therefore, it is desirable to reduce the amount of rare-earth magnets in motors and generators.
For example, a patent document 1 (i.e., Japanese Patent Laid-Open No. 2010-252530) discloses a consequent-pole type rotor in which a permanent magnet is positioned within every other pole. That is, when the first and second salient poles are alternatively arranged in a circumferential direction, a permanent magnet is only positioned in the first salient pole. In such a consequent-pole type rotor, the second salient pole is “consequently” magnetized to have an inner face side pole of the permanent magnet that is buried in the adjacent salient pole, which results in an alternative arrangement of N poles and S poles on the rotor's surface. As a result, the number of permanent magnets is reduced in half, thereby simultaneously reducing cost and procurement risk.
However, a consequent-pole type rotor may suffer from cogging torque due to the interaction between the permanent magnets. As a result, cogging torque may produce torque output fluctuations at low speeds and reduce motor efficiency.
The magnitude of the cogging torque depends upon the dimension of the motor components. More specifically, the magnetic flux distribution in a gap between a stator and a rotor of a motor is controlled and determined only by a main component having a high-frequency variation, which may also be designated as a space order component having the same number as the number of teeth on the stator, if other and/or accompanying components of the cogging torque having lower frequencies are sufficiently decreased. Therefore, the distribution of the magnetic fluxes, respectively departing from a permanent magnetic pole and landing on a soft magnetic material pole, substantially controlled by the high frequency variation of the cogging torque has a smaller variation amplitude, thereby resulting in a smaller magnitude of the cogging torque due to a smaller variation of attractive force that attracts the rotor.
The magnitude of cogging torque that is generated by a skewed distribution of the magnetic flux is correlated to a space order of the magnetic flux, that is, to a frequency of change of the magnetic flux in time. That is, the smaller the frequency of the change of a certain subject space order is, the greater the amplitude of the component of the cogging torque in the subject space order would be. Therefore, ideally, the main component of the magnetic flux is maximized for the reduction/removal of the other lower-order components of the magnetic flux.
For example, when the number of teeth of the stator is 12, a main component of the cogging torque has a 12th order, and when the number of teeth is 48, a main component of the cogging torque has a 48th order. In such case, the cogging torque is preferably designed to include as few other lower-order components as possible. This occurs because the amplitude of vibration becomes smaller for higher frequency when an excitation energy is constant.